The Excel PMT Function

Basic Description

The Excel PMT function calculates the constant periodic payment required to pay off (or partially pay off) a loan or investment, with a constant interest rate, over a specified period.

The syntax of the function is:

PMT( rate, nper, pv, [fv], [type] )

Where the arguments are as follows:

rate

-

The interest rate, per period.

nper

-

The number of periods over which the loan or investment is to be paid.

pv

-

The present value of the loan / investment.

[fv]

-

An optional argument that specifies the future value of the loan / investment, at the end of nper payments.

If omitted, [fv] has the default value of 0.

[type]

-

An optional argument that defines whether the payment is made at the start or the end of the period.

The [type] argument can have the value 0 or 1, meaning:

0 - the payment is made at the end of the period;1 - the payment is made at the beginning of the period.

If the [type] argument is omitted, it takes on the default value of 0 (denoting payments made at the end of the period).

Cash Flow Convention:

Note that, in line with the general cash flow convention, outgoing payments are represented by negative numbers and incoming payments are represented by positive numbers. This is seen in the examples below.

Excel Pmt Function Examples

Example 1

In the following spreadsheet, the Excel Pmt function is used to calculate the monthly payments on a loan of $50,000 which is to be paid off in full after 5 years. Interest is charged at a rate of 5% per year and the payment to the loan is to be made at the end of each month.

Formula:

A

1

Monthly payments on a loan of$50,000 that is to be paid off infull over 5 years, with an interestrate of 5% per year (paymentmade at end of each mth):

2

=PMT( 5%/12, 60, 50000 )

Result:

A

1

Monthly payments on a loan of$50,000 that is to be paid off infull over 5 years, with an interestrate of 5% per year (paymentmade at end of each mth):

2

-943.56

Note that in this example:

The payments are made monthly, so the annual interest rate of 5% has been converted into the monthly rate (=5%/12), and the period of 5 years is expressed in months (=5*12).

As the future value is zero, and the payment is to be made at the end of the month, the [fv] and [type] arguments can be omitted from the above function.

The value returned from the function is negative, as this represents an outgoing payment (for the individual taking out the loan).

Example 2

In the spreadsheet below, the Excel Pmt function is used to calculate the quarterly payments required to increase an investment from $0 to $5,000 over a period of 2 years. Interest is paid at a rate of 3.5% per year and the payment into the investment is to be made at the beginning of each quarter.

Formula:

A

1

Quarterly payments into an investmentwith current value $0, which isrequired to reach $5,000 over 2 yrs.The interest rate is 3.5% per year(payment made at start of each qtr):

2

=PMT( 3.5%/4, 8, 0, 5000, 1 )

Result:

A

1

Quarterly payments into an investmentwith current value $0, which isrequired to reach $5,000 over 2 yrs.The interest rate is 3.5% per year(payment made at start of each qtr):

2

-600.85

Note that, in this example:

The payments into the investment are made quarterly, so the annual interest rate of 3.5% is converted into a quarterly rate (3.5%/4), and the number of years is converted into quarters (=2*4).

The [type] argument has been set to 1, to indicate that the payment into the investment is to be made at the beginning of each quarter.

The value returned from the function is negative, as this represents an outgoing payment.